Quantum phases of Bose gases on a lattice with pair-tunneling

We investigate the strongly interacting lattice Bose gases on a lattice with two-body interaction of nearest neighbors characterized by pair tunneling.The excitation spectrum and the depletion of the condensate of lattice Bose gases are investigated using the Bogoliubov transformation method and the results show that there is a pair condensate as well as a single particle condensate.The various possible quantum phases,such as the Mott-insulator phase(MI),the superfluid phase(SF) of an individual atom,the charge density wave phase(CDW),the supersolid phase(SS),the pair-superfluid(PSF) phase,and the pair-supersolid phase(PSS) are discussed in different parametric regions within our extended Bose-Hubbard model using perturbation theory.